Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
426 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20265849 | C2 | semidirect |
| 2. #20265525 | C2 | semidirect |
| 3. #20265454 | C2 | semidirect |
| 4. #20265372 | C2 | semidirect |
| 5. Q8×#11717579 | C2 | semidirect |
| 6. C4×#13108059 | C2 | semidirect |
| 7. D4×Q8×C101 | C2 | semidirect |
| 47. Q8×C101 | D8 | semidirect |
| 49. D4×C101 | #41 | semidirect |
| 82. C101 | #3358 | semidirect |
| 84. D4×Q8 | D101 | semidirect |
| 129. Q8 | #13108059 | semidirect |
| 135. D4 | #13108075 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265849 | 2 |
| #20265525 | 2 |
| #20265454 | 2 |
| #20265372 | 2 |
| Q8×#11717579 | 2 |
| C4×#13108059 | 2 |
| D4×Q8×C101 | 2 |
| #3358 | 101 |